CN2106 Transport Phenomena

Interactive lecture-by-lecture guide. Select a part, then click a lecture to explore its key concepts and equations.

Part 1 — Fluid Mechanics

L1–L8 · Prof. Jiang Jianwen

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STEP 1FUNDAMENTAL CONCEPTS

L1 — Fluids, viscosity, stress & the continuum hypothesis

Transport Phenomena begins with the question: what IS a fluid? A fluid is any substance that deforms continuously under an applied shear stress — it cannot resist shear at rest. This lecture establishes the continuum hypothesis, the key fluid properties, and the Reynolds Transport Theorem (RTT) which is the master equation linking system-based conservation laws to a fixed control volume.

Fluids include both liquids and gases. The defining property is that they cannot sustain shear stress at rest — they flow. This is contrasted with solids, which can resist shear.

Continuum HypothesisFoundational assumption

We treat the fluid as a continuous medium, ignoring its discrete molecular structure. This is valid when the length scales of the problem are much larger than the mean free path of molecules. The continuum assumption breaks down in rarefied gas flows (very low pressure) or nano-scale flows.

Density ρFluid property

Mass per unit volume. For an incompressible liquid, ρ is essentially constant. For ideal gases, ρ = PM/(RT) varies with pressure and temperature. Density appears in every conservation equation.

ρ=mV[kg/m3]\rho = \frac{m}{V} \quad [\text{kg/m}^3]
Dynamic Viscosity μFluid property

Viscosity measures a fluid's resistance to shear deformation. For a Newtonian fluid, the shear stress τ is linearly proportional to the velocity gradient (rate of strain). This is Newton's law of viscosity — the defining equation for Newtonian fluids.

τ=μdudy[Pa]\tau = \mu \frac{du}{dy} \quad [\text{Pa}]

μ in Pa·s; for water μ ≈ 10⁻³ Pa·s, for air μ ≈ 1.8×10⁻⁵ Pa·s at 20°C.

Kinematic Viscosity νFluid property

The ratio of dynamic viscosity to density. Kinematic viscosity appears naturally in the Reynolds number and Navier-Stokes equations. It represents the diffusivity of momentum.

ν=μρ[m2/s]\nu = \frac{\mu}{\rho} \quad [\text{m}^2/\text{s}]
Reynolds Number ReDimensionless group

The ratio of inertial forces to viscous forces. Re is the most important dimensionless number in fluid mechanics — it determines whether a flow is laminar (ordered, low Re) or turbulent (chaotic, high Re). For pipe flow: Re < 2300 laminar, Re > 4000 turbulent.

Re=ρVLμ=VLνRe = \frac{\rho V L}{\mu} = \frac{VL}{\nu}
CN2106 — Quick Check
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Q1.The Hagen-Poiseuille equation for laminar pipe flow gives volumetric flow rate Q as: